This seems awfully speculative. Let's take a look at their reasoning:
Yes, it is true that per C-USA by-laws, they will not be attending any of the five bowl games that C-USA is affiliated with. The conference has five affiliations and they are tied with MTSU for the sixth best record in the conference.
It is also true that there are currently 79 eligible teams for 76 bowl slots, with the possibility of two more teams - Temple and Oklahoma State - joining the fray with one more win.
However, even if those two teams win, UAB is still one of eighteen bowl eligible teams with a 6-6 record. Only one of those teams (South Alabama) is already guaranteed a bowl game, and you can't tell me that the Blazers are significantly far behind any other team in that grouping with regard to what the selection folks will look at.
Will this team play the best game they've ever played? Of course they will, it's literally their "there is no tomorrow" game. Will their fans travel? You better believe it, for the same reasons, plus the opportunity to shove the assumption that their fans don't care about them in everyone's faces.
I'm not saying it's guaranteed that they will get a bowl game, but it is far from certain that they won't.